The present invention relates to object fabrication systems in general and in particular to fabrication of objects using a plurality of base materials and a device that can place base material under computer or electronic device command.
Many objects have properties that depend on the material they are constructed from. For example, marble statues are hard and feather pillows are soft. Often, the properties of an object are assumed to be fixed and determined by their construction. For example, the color of a loaf of bread is expected to be white, tan or brown. The shape of is also often determined by the method of manufacture—bread is usually round or loaf-shaped, crusty on the outside and soft on the inside, all as a result of the need for a pan to hold the bread and the fact that the oven's heat hits the outside surface more than the inside.
It has long been known in the field of computer graphics that computer models and image generators can free users from the constraints of physics—it is easy to generate a video of a talking animal, a floating loaf of bread, impossible physics, etc. Thus, by providing the appropriate instructions, an animation system can output a video sequence that is created entirely from the instructions and is thus not constrained by physical construction methods.
What computer graphics has done to movies, 3D printers have done to objects. Albeit with some constraints, it is possible to send a set of computer instructions to a 3D printer to print objects of arbitrary shapes, even some objects that would be otherwise impossible to create using manual techniques for object creation, such as mold casting, carving, milling, etc.
3D printers have been used to generate prototypes, models and curios, but have been limited in that while the ultimate shape of the object can be arbitrarily specified by a computer (or a user using a computer interface to the 3D printer), the object will be homogeneous because it is all made of whatever output material (resin, plastic, etc.) that particular printer uses. Of course, there is not total freedom, because some instructions might result in collapse of the object's parts if there is not enough support.
Some objects are elastically deformable and their interest as objects is that they have those properties. For example, a soccer ball that did not elastically deform would not be of interest as a soccer ball per se. Other examples include garments and shoes, furniture, plants, or even human or animal tissue. In both the animation context and in real-world object creation context, obtaining the correct object characteristics, determining characteristics of materials used and other characterizations are important to know. In animation, the problem is easier, since the behavior of virtual objects need not comply with the laws of physics, whereas physical objects do and their behavior is largely constrained to their construction—a virtual bouncing ball can be made of stone, but a physical object ball made of stone simply will not bounce.
Deformation effects can be modeled at very diverse scales, ranging from molecular interactions to globally-supported response functions, and through continuum elasticity laws or lumped-parameter models [Zohdi and Wriggers 2004]. As recently demonstrated by work in numerical coarsening and homogenization, the behavior of materials with microscale inhomogeneities can be approximated by mesoscale homogeneous materials [Kharevych et al. 2009].
In some 3D printers, there is one consumable material (rubber, plastic, resin, etc.) and the output objects are made of 100% of that consumable material. Recent developments, however, include multi-material 3D printers such as the OBJET™ Connex™ series 3D printers. These printers can “print” objects that include components made of a first material and components made of a second material, where the two (or more) materials vary in some parameter, such as density, elasticity, hardness, etc.
The computer graphics field has already contributed systems for designing and fabricating virtual clothes [Okabe et al. 1992], plush objects [Mori and Igarashi 2007], paper craft objects [Mitani and Suzuki 2004], or surface microgeometry [Weyrich et al. 2009].
What is needed is the ability to create deformable objects (or objects with other sets of characteristics) from computer instructions to match some desired user-specified characteristics. Of course, if the desired characteristics are the characteristics provided by the consumable material, the problem is simple, but often users will have more complex needs.
In the context of computer graphics, simulation of soft tissue using finite element models is known, as is data-driven modeling of deformable virtual materials. A recent survey of deformation models in computer graphics is shown in [Nealen 2006].
A popular approach for accurately modeling deformable materials in computer graphics uses continuum elasticity laws together with finite element modeling. This approach is capable of modeling a large range of materials, including those with nonlinear and heterogeneous deformation behavior. Typically, one must select a constitutive material model [Ogden 1997] that is capable of covering the range of behaviors of the material, and then, given a certain object and constitutive model, the material parameters are tuned in order to fit empirical data. This approach was introduced to bio-mechanical modeling in computer graphics by Terzopoulos et al. [1987], and it has been later applied to body parts such as the face [Koch et al. 1996; Magnenat-Thalmann et al. 2002; Terzopoulus and Waters 1993; Sifakis et al. 2005], the hand [Sueda et al. 2008], the neck [Lee and Terzopoulos 2006], the torso [Zordan et al. 2004; Teran et al. 2005; DiLorenzo et al. 2008] or the complete upper body [Lee et al. 2009]; to the simulation of fracture effects [O'Brien and Hodgins 1999]; or even interactive simulation after a model reduction step [Barbi{hacek over (c)} and James 2005].
In order to achieve high realism, continuum elasticity approaches rely on complex processes involving accurate modeling of the geometry and fine tuning of parameters.
Several researchers have designed methods to automatically identify the parameters of constitutive models from measurements of real objects. These measurement-based modeling approaches cover the estimation of parameters such as Young modulus [Schnur and Zabaras 1992], both Young modulus and Poisson ratio together [Becker and Teschner 2007], non-linearly interpolated Young modulus and Poisson ratio [Bickel et al. 2009], plasticity parameters [Kajberg and Lindkvist 2004], or non-linear viscoelasticity parameters [Kauer et al. 2002].
Other measurement-based modeling approaches, instead of estimating local parameters, fit directly globally-supported functions as material description. Pai et al. [2001] introduced a system for capturing in a unified framework an object's shape, its elasticity, and roughness features. They used a Green's functions matrix representation [James and Pai 1999] in order to describe the deformation model. Later, others have extended the work of Pai et al. to increase robustness and handle viscoelastic effects [Lang et al. 2002; Schoner et al. 2004].
Recent work in computer graphics aims at modeling high-resolution heterogeneities even when the resolution of the discretization is considerably coarser [Kharevych et al. 2009; Nesme et al. 2009]. This process, known as homogenization, tries to find parameter values of a constitutive model sampled at low resolution such that the behavior of the object best matches the heterogeneous material. However, it is one thing to create an object seen only on the screen and another thing to create a physical object.